Econometrics I

What is Econometrics?

• Theoretical economic models explain the qualitative relationship between different economic variables

  • e.g., Consumption is expected to increase as disposable income and wealth increase (positive relationship)

• However, few models indicate the magnitude of the relationship

  • Yet this is what matters most to policymakers.

  • Central bankers need to know how much a 1 percentage increase in the interest rates will have on inflation and the growth rate of the economy

What is Econometrics?

Econometrics uses economic theory, mathematics, and statistical inference to quantify economic phenomena

• The objective of econometrics is to convert qualitative statements into quantitative statements

• the relationship between two or more variables is positive vs. consumption expenditure increases by 95 cents for every one dollar increase in disposable income

Source

The Challenge

• The gold standard for drawing inferences about the effect of a policy is a randomized controlled experiment

• However, in many cases, experiments remain difficult or impossible to implement

  • for financial, political, or ethical reasons, or because the population of interest is too small.

Source

The Challenge

• Unethical: Prevent potential students from attending college in order to study the causal effect of college attendance on labor market experiences,

• Politically infeasible: Study the effect of the minimum wage by randomly assigning minimum wage policies to states.

The Challenge

• A large share of the empirical work in economics about policy questions relies on observational data

  — data where policies were determined in a way other than through random assignment

• Drawing inferences about the causal effect of a policy from observational data is challenging

Minimum Wage Example

To understand the challenges, consider the example of the minimum wage. A naive analysis of the observational data might compare the average employment level of states with a high minimum wage to that of states with a low minimum wage. This difference is surely not a credible estimate of the causal effect of a higher minimum wage, defined as the change in employment that would occur if the low-wage states raised their minimum wage. For example, it might be the case that states with higher costs of living, as well as more price-insensitive consumers, choose higher levels of the minimum wage compared to states with lower costs of living and more price-sensitive consumers.

Confounders

• These factors, which may be unobserved, are said to be confounders

• Confounders induce correlation between minimum wage policies (explanatory variable) and employment (response variable) that is not indicative of what would happen if the minimum wage policy changed

Confounders

Figure 1: Education -> Earnings; Mental Ability -> Education & Earnings

Identification Strategies

• In economics, researchers use a wide variety of strategies for attempting to draw causal inference from observational data

• These strategies are often referred to as identification strategies or empirical strategies, because they are strategies for identifying the causal effect

• We say, somewhat loosely, that a causal effect is identified if it can be learned when the dataset is sufficiently large.

Machine Learning and Econometrics

• Supervised machine learning focuses primarily on prediction problems

• Unsupervised machine learning focuses on methods for finding patterns in data, such as groups of similar items, like clustering images into groups, or putting text documents into groups of similar documents.

ML vs Econometrics

• ML approach is fundamentally different from the goal of causal inference in observational studies,
  • where we observe data on outcomes and a treatment variable, and we wish to draw inferences about potential outcomes
• the main focus of supervised machine learning is on prediction performance without regard to the implications for inference

ML vs Econometrics

• supervised machine learning methods typically rely on data-driven model selection, most commonly through cross-validation,

• in econometrics, the model is informed by economic theory

ML vs Econometrics

Stages of Development

1. By relying on economic theory, formulate a hypothesis to explain the data being examined
2. Develop an identification strategy to account for confounders
3. Apply the identification strategy to test the hypothesis using statistical tools

• Focus of this course is to introduce the statitical tools